Simultaneous Advance for Extended MHD with Kinetic Closures: Verification and Applications

We present progress on a simultaneous time-advance of NIMROD's fluid quantities with consistent kinetic closures obtained from a solution of the Chapman-Enskog-like drift kinetic equation. A semi-implicit formulation is employed to ensure numerical stability and accommodate time steps that are large compared to the compressional Alfven wave propagation time.

In this study, we expand upon previous research, which laid the foundation for a simultaneous advance of fluid and kinetic quantities in NIMROD. Using a leap-frog method, the center-of-mass flow is staggered in time from other fluid quantities. This enhances numerical stability. Our current work extends this approach to include the simultaneous advancement of electron and ion velocity distribution functions. A Newton-Krylov technique is utilized to solve for the ion and electron temperatures in conjunction with the kinetic distortion.

We present results from linear and nonlinear verification simulations of ion-acoustic waves, comparing the measured frequencies and Landau damping rates with theory. Our simulations also include collisional effects, whereas prior treatments of ion-acoustic waves focus on solutions to the Vlasov equation. In a separate study, we incorporate the kinetic electron stress in Ohm's law to study the hybrid fluid/CEL-kinetic prediction of the bootstrap current in tokamaks. Our findings provide valuable insight into the behavior of magnetized plasmas in the long mean free path regime.